The QPE algorithm [1]} can be thought of as a projection of an input state (called the reference state or the initial state interchangeably) onto an eigenstate, whose eigenvalue we then compute with the algorithm. This necessitates the initially prepared reference state having at least a non-negligible overlap with the exact eigenstate of the Hamiltonian, and hence
preparation of a good initial state is of utmost importance. There have been a number of works in literature that have addressed the issue of constructing an initial state that has substantial overlap with the eigenstate of the system Hamiltonian. In the molecular weak correlation regime, the simplest choice, namely the single determinant Hartree-Fock (HF) function, often serves this purpose quite well. However, this is often not the case while dealing with strongly correlated systems, and in such scenarios, using a combination of multiple Stater determinants as the initial
reference function becomes very important. This line of thought has led various authors to construct the initial state by various means, for example, by employing the classically computed Complete Active Space Self-Consistent Field method [2]}, [3]} or using Adaptive Sampling CI [4]} techniques. Both of these approaches have shown substantial squared overlap of the initial reference state with the eigenstate of the Hamiltonian, and thus a high probability of success for the QPE algorithm. Sugisaki et. al. [5]} have computed the reference state by exploiting the diradical characters of the molecules from a spin-projected Unrestricted HF wavefunctions. This method entirely bypasses any post-HF calculations for the
reference state preparation, and drastically improves the success probability of QPE, particularly for molecules with intermediate diradical characters. A complementary
approach for initial state preparation is often followed, where the HF Hamiltonian is slowly and systematically changed over to the FCI Hamiltonian, such that the system remains in its instantaneous ground state. This is known as the Adiabatic State Preparation (ASP) in literature [6]}.
